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Extensions of asymptotic fields via meromorphic functions

Shackell, John (1995) Extensions of asymptotic fields via meromorphic functions. Journal of the London Mathematical Society, 52 (part 2). pp. 356-374. ISSN 0024-6107. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:19037)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.

Abstract

An asymptotic field is a special type of Hardy field in which, module an oracle for constants, one can determine asymptotic behaviour of elements. In a previous paper, it was shown in particular that limits of real Liouvillian functions can thereby be computed. Let F denote an asymptotic field and let f is an element of F. We prove here that if G is meromorphic at the limit of f (which may be infinite) and satisfies an algebraic differential equation over R(x), then F(Gof) is an asymptotic field. Hence it is possible (module an oracle for constants) to compute asymptotic forms for elements of F(Gof). An example is given to show that the result may fail if G has an essential singularity at limf.

Item Type: Article
Subjects: Q Science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: I.T. Ekpo
Date Deposited: 31 Oct 2009 15:43 UTC
Last Modified: 16 Nov 2021 09:57 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/19037 (The current URI for this page, for reference purposes)

University of Kent Author Information

Shackell, John.

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